From JP 2005052912, a machine for finish machining of camshafts is known. To simultaneously machine all the cams, a corresponding number of finishers are positioned around the camshaft. As a result, the operating personnel can only access the machine with difficulty. In addition, the camshaft cannot be supported with steady rests, as the space needed for them is occupied by the finishers. Hence the machine is not suitable for grinding at high removal rates. Moreover, for loading and unloading, multi-axial sequences of motion are required because the camshafts have to be moved into the working area or out of the working area lengthwise. EP 0,085225 [U.S. Pat. No. 4,443,976] shows a method of grinding camshafts in which a uniform feed speed is achieved by adapting the speed of rotation of the camshaft to the cam shape. According to this method, the cams are individually machined one after the other.